The Fe Kα line

Fe K

L N

L X-ray

Fe K

M M

N X-ray

Figure 1.6: The Kαtransition for iron occurs when an energetic X-ray photon ejects an electron from the Fe K-shell. A photon at 6.4 keV is then emitted when an electron from the L-shell fills the hole left by the K-shell electron. (Image produced with Inkscape.)

1.4 AGN in the X-ray 21

ionization state from neutral Fe (FeI) to FeXXIII. From Lithium-like to Hydrogen-like Fe atoms (FeXXIV to FeXXVI) the absence of more than two electrons from the L-shell means that the Auger effect can not occur. For FeXXV and FeXXVI ions, the fluorescence line is produced when a free electron is captured by the atom (recombination) (Matt et al. 1997). For neutral Fe atoms, the fluorescence yield is proportional to the atomic number to the power of four (∝Z⁴), making the Fe Kαemission particularly strong (Fabian et al. 1989;Matt et al. 1997;Fabian et al.

2000). For cosmic abundances of Fe, the optical depth of bound-free Fe absorption is close to the Thomson depth. Hence, the Fe Kαline production of an X-ray irradiated slab takes place in the outer Thomson depth. This is only a fraction of the total thickness of the slab (0.1% to 1%) and depends on the ionization state of the gas in this thin region(Fabian et al. 2000).

Fe Kα is an intrinsically narrow line, with energy with ∼3.5 eV (Laor 1991; Fabian et al.

2000; Ricci et al. 2014), which is much smaller than current satellite spectral resolution (e.g.

XMM-Newtonhas a spectral resolution of∼150 eV at 6.4 keV). In a Newtonian, non-relativistic disc, the Fe Kαline would have a perfectly symmetrical double-horned profile due to the Doppler shift of the radiation emitted by the approaching (blue-shifted) and receiving (red-shifted) edges of the accretion disc (Fabian et al. 1989;Laor 1991;Fabian et al. 2000). The broadness of the line in this case would be determined by the velocity of the matter rotating at the innermost disc radius, which is the highest speed. However, the presence of the SMBH introduces relativistic effects that influence further the line profile. Special relativistic beaming enhances the blue peak of the line from every radius of the accretion disc. Transverse Doppler effect and gravitational redshift determine that photons can leave the gravitational potential of a BH only by losing energy thus shifting Fe Kαemission from every radius to lower energies. The sum of the contributed emission from all the accretion disc radii results in a skewed and highly broadened line profile (see Figure 1.7) (Fabian et al. 1989;Laor 1991; Bromley et al. 1998; Pariev & Bromley 1998;

Martocchia et al. 2000).

The shape of the line profile is also determined by the metric of the spacetime. In the Shwarzschild metric

νobs

νem

= r

1− 2

r, (1.9)

where νem is the emitted frequency, νobs is the observed frequency at infinity and r is the emission radius. In the Kerr metric, the gravitational redshift is defined as

νobs

νem

= r

1− 2r

r²+a², (1.10)

however, this holds only for the photon emitted on the rotation axis (θ=0). Eq. 1.10 shows, that by increasing BH spin, the energy width of the Fe Kαline will also increase.

The profile of the Fe Kαline is also affected by the geometry of the matter surrounding the SMBH (Laor 1991;Brenneman & Reynolds 2006;Dauser et al. 2010, e.g.). The extended high-energy wing of the feature is a strong function of the angle between the normal to the accretion disc and the line of sight, which from now on we will refer to as the inclination angle. At low

4 5 6 7 8 9 Energy [keV]

10^-1 10⁰

Countss−1keV−1

Incl =5°, a =0 Incl =30°, a =0 Incl =75°, a =0

4 5 6 7 8 9

Energy [keV]

10^-1 10⁰

Countss−1 keV−1

Incl =5°, a =1 Incl =30°, a =1 Incl =75°, a =1

Figure 1.7: The Fe K αline is intrinsically narrow but its profile is broadened and skewed by the relativistic Doppler effect and gravity. The line profile depends on the geometry of the disc, thus inclination with respect to the line of sight, and spin of the BH. For this reason, the Fe Kα line profile is a diagnostic of relativistic signatures of SMBH and a great tool to test the AGN unification model.

inclination angles the observer views the disk almost face-on. In this case, the observer will see almost nothing of the rotation of the disk and there will be no large velocity component.

In contrast, at high inclination angles, the observer sees the approaching and receding parts of the disk. In this case, the high-energy extent is increased by relativistic boosting and the line will appear to be double-horned (Fabian et al. 1989; Fabian et al. 2000) (see Fig. 1.7). High disc inclinations imply that the emission from the innermost regions of the disc is shielded and absorbed by the molecular torus (see Section 1.2). In the case of a toroidal uniformly distributed as predicted by the unification theory of AGN we would never be able to observe relativistic broadened Fe Kαlines in AGN with high column density and high disc inclinations. If however, we assume a clumpy molecular torus, then it would be possible to observe some radiation from the disc from the gaps in the torus. Thus, the relation between the broadening of the Fe Kαline and the disc inclination can be used as a test of the unification theory of AGN and to probe the geometry of the matter surrounding the SMBH (Zhang et al. 2008;Ricci et al. 2014).

The intensity of the Fe Kα line (and of the reflection component in general) might also reveal the geometry of the corona of relativistic electrons emitting the primary X-ray continuum (see Fig. 1.4) (Fabian et al. 2000;Ballantyne & Fabian 2003). In fact, different corona shapes determine how much X-ray radiation is reflected by the disc and thus how strong is the observed reflection component. Stronger reflection is observed in the case of a lamp-post geometry, where the height of the point source is larger than r_g(Bambi 2017).

The theory attributing relativistic effects to the broadness of the Fe Kαlines is widespread yet not unequivocally proven. Alternative hypotheses suggest that the broadening of the Fe Kαline is artificially introduced when the X-ray continuum is absorbed (e.g.Miller et al. 2008). In fact,

1.4 AGN in the X-ray 23 AGN showing a broadened Fe Kαemission line often present signs of absorption from several layers of ionized gas and ionized outflowing winds (Nandra et al. 2007;Miller et al. 2007,2008).

Distinguishing these requires high quality X-ray data.

The presence of broadened Fe Kαlines is well documented especially in bright AGN in the nearby Universe (e.g. MCG–6-30-15Tanaka et al. 1995;Miller et al. 2002). However, there are some objects in which the broad Fe Kαline is not detectable (Gondoin et al. 2003;Pounds et al.

2003).

Relativistic lines are expected to be ubiquitous if we assume a standard scenario where the SMBH is surrounded by an accretion disc and a hot corona of electrons (Nandra et al. 2007;

Guainazzi et al. 2006;Mantovani et al. 2014). The fact that these features are not always found is hard to explain. A possible reason for this could be that the matter in the disc is ionized.

Indeed, it is reasonable to expect some degree of ionization, especially at large accretion rates.

A strong reduction of the line flux is expected for moderate ionization due to resonant trapping.

At very large degrees of ionization, the matter is fully ionized and no fluorescent line is emitted (Fabian et al. 2000). For a given BH mass M, the ionization parameter (L/ηr²) increases with luminosity. However, at fixed Eddington ratio, the ionization parameter decreases with the BH mass, hence its luminosity. It would be important to search for relations between the presence of the broad Fe Kαline and the luminosity or the accretion rate.

Another reason not to detect broad lines could be an accretion disc truncated well before the last stable orbit. It could also be possible that the broad line is present but so broadened to make it hard to detect, especially in faint sources (Guainazzi et al. 2006;Mantovani et al. 2014).

An interesting aspect of the Fe Kαline that could also explain why sometimes this feature is not detected is the anti-correlation between the line energy width (EW) and the luminosity of the X-ray continuum, called the Iwasawa-Taniguchi or X-ray Baldwin effect. Observed for the first time by Iwasawa & Taniguchi (1993), this anti-correlation has been confirmed several times and has been linked to the receding of the molecular torus at high luminosity. The same effect for the broad Fe Kαline was proposed for the first time inNandra et al. (1997b), but not subsequently confirmed. The physical origin of the Baldwin effect for the broad wings of the line is very different from the one producing the anti-correlation for the narrow core. The broad component arises in the rings of the accretion disc closer to the ISCO and the central SMBH. A strong AGN luminosity could imply a higher ionization rate of the disc and in the most extreme scenarios the receding of the disc itself, which would suppress the emission of the Fe Kα line from those regions.

Detecting the Baldwin effect for the broad component of the Fe Kαline and disentangling it from the Baldwin effect for the narrow component would provide important insights on the geometry of the disc and molecular torus (Nandra et al. 1997b).

To sum up, the Fe Kα line is one of the most insightful features in the X-ray spectrum of AGN. The strong dependency of the line profile with spin and inclination angle of the disc makes it the perfect tool to probe the relativistic effects due to the proximity of the SMBH, the mode of BH accretion, and the unification theory of AGN. Studying the profile of the Fe Kαline could also solve open issues like the structure of the molecular torus and the geometry of the relativistic corona emitting the X-ray primary continuum.